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Inter-industry Wage Differentials andAllocative InefficiencyAnders Sørensen aa Copenhagen Business School and CEBRPublished online: 16 Mar 2007.

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International Economic JournalVol. 21, No. 1, 1–26, March 2007

Inter-industry Wage Differentials andAllocative Inefficiency

ANDERS SØRENSEN

Copenhagen Business School and CEBR

ABSTRACT Do inter-industry wage differentials reveal information on allocative ineffi-ciency, implying that reallocation of labor input from low- to high-wage sectors improvesaggregate productivity? This question is addressed by introducing wage-weighted averages ofsector employment growth in growth regressions using panel data for selected OECD coun-tries over the period 1971-93. For the 1970s, it is found that reallocation of labor betweensectors with different wages did not contribute to explaining economic growth, whereas itdid for the 1980s. Hence, observable wage differentials only reflect allocative inefficiencyafter 1980.

KEY WORDS: Inter-industry wage differentials, growthJEL CLASSIFICATION: O11, O30, J30

Introduction

Economic efficiency increases when labor is reallocated from sectors with low, tosectors with high, marginal value products of labor. Since marginal value productsare unobservable, it is relevant to ask if observable sector wages contain informa-tion on allocative inefficiency. This is not certain since part of labor remunerationpotentially consists of labor rents that come on top of marginal value products.Katz & Summers (1989) discuss allocative inefficiency when sectors operate ontheir labor demand curve, i.e., when observable wages equal marginal value prod-ucts, implying that aggregate productivity increases through reallocation of laborfrom low- to high-wage sectors.1 On the contrary, this may not be the case whensectors operate off their labor demand curves. Only when mark-ups of wagesover marginal value products are invariant across sectors, such that observable

Correspondence Address: Anders Sørensen, Porcelænshaven 16A, 2nd floor, DK-2000 Frederiksberg,Denmark. Email: as.eco@cbs.dk1See Katz & Summers (1989, pp. 248–254).

1016-8737 Print/1743-517X Online/07/010001–26 © 2007 Korea International Economic AssociationDOI: 10.1080/10168730601180994

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2 A. Sørensen

relative wages equal relative marginal value products, do wage differentials reflectallocative inefficiency.

This paper investigates whether aggregate productivity is affected throughreallocation of labor between sectors with different wages by introducing areallocation index in growth regressions. The reallocation index is defined as aweighted average of sector employment growth rates using sector wage differen-tials as weights. If the reallocation index enters positively and significantly,reallocation of labor from low- to high-wage sectors improves economic efficiency.The main finding is that a changing employment structure towards high-wage sec-tors affects aggregate productivity growth positively and significantly in the 1980sfor selected OECD countries, whereas such changes did not play a significant roleduring the 1970s. Hence, wage differentials across sectors contain informationon allocative inefficiency during the 1980s but not during the 1970s.

An important objection to the main finding is that the association between theemployment structure and aggregate productivity may not represent the causalrelationship, where reallocation of labor between sectors with different wagesaffects aggregate productivity. It is possible, for example, that sectoral produc-tivity changes in the 1980s are biased towards high-wage sectors for exogenousreasons, and it is those sectors that expand and draw labor. In this case, a pos-itive and significant effect on aggregate productivity of a changing employmentstructure towards high-wage sectors can arise even when inter-industry wagedifferentials do not reflect marginal value products of labor.

The issue of endogeneity is addressed by introducing an instrument variableand using two-stage least square estimation. The instrument variable is based onthe separability assumption of intermediate inputs and value-added in sectoralgross output; see for example Arrow (1974). Due to separability, an increase inintermediate inputs has a direct positive effect on gross output but no directeffect on value-added. However, it seems plausible that intermediate input ispositively correlated with primary factor inputs, especially labor input, implyingthat data on intermediate input can be used to construct an instrument variable.An alternative method used to address endogeneity is to investigate whether sectorproductivity growth rates and sector wages are positively correlated. The resultsof these analyses suggest that endogeneity is not an extensive problem.

The persistence of inter-industry wage differentials is a well-known pheno-menon in developed countries. There are two main explanations for thesedifferences. First, wage differentials appear to be affected by competitive forces.Factors that are believed to be of substantial relevance are the innate ability andhuman capital of workers; see Abowd et al. (1999a, 1999b), Juhn et al. (1993),and Neal (1995). Second, wage differentials arise partially due to rents from non-competitive forces or labor market institutions, see for example Katz & Summers(1989), Blanchflower et al. (1996), and Katz & Autor (1999). It is important toemphasize that wages can include rents either as rents added on top of marginalvalue products or as rents included in marginal value products with the latter caseoccurring when workers are able to set wages that equal marginal value productsabove the wage rate for perfect competitive labor markets. If the former definitionof rents holds, sectors operate off the labor demand curve, implying that sec-tor wages are not likely to reflect allocative inefficiency, whereas they operate on

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Inter-industry Wage Differentials and Allocative Inefficiency 3

the labor demand curve if the latter definition holds, implying that sector wagesshould reflect allocative inefficiency.

The main finding of this paper raises the important question of why wagedifferentials across sectors reflected inefficiencies during the 1980s but not the1970s. The finding is consistent with the view that a regime shift for the wage-setting behavior took place: in the 1970s inter-industry wage differentials, to ahigh degree, arose from variation in the part of labor remuneration that consistsof rents added on top of marginal value products, whereas to a higher degreethey reflected differences in marginal value products in the 1980s. Moreover, theresult is consistent with the perception that competition pressure has increasedin product markets between the two decades, leading to lower levels of profits tobe shared with workers.

Rodrik (1997) argues that the bargaining power of unskilled labor erodes asa consequence of globalization, implying that labor rents may have fallen indeveloped countries. The suggested mechanism is that outsourcing has increasedthe substitutability of unskilled labors2. An alternative explanation is that skill-biased technological changes reduce bargaining power because such changesincrease the competitive, wage rate of skilled workers and thereby underminethe coalition between skilled and unskilled workers in the support of unions, seeAcemoglu et al. (2001). Both explanations lead to a decreasing relative wage ofunskilled labor due to falling labor rents.

Several other authors are favorable to the view that the wage-setting beha-vior changed around 1980 in the United States: Borjas & Ramey (1995) suggestthat it may have changed for the entire economy as a con-sequence of glob-alization; Bertrand (2004) find evidence consistent with increased competitionto cause a shift away from implicit agreements that protect wages from exter-nal labor-market conditions, Howell (1994) argues that the wage-setting practicechanged fundamentally at the end of the 1970s; and Mitchell (1985) documents a‘norm shift’ in wage determination in the early 1980s. Furthermore, Wallerstein &Western (2000) argue that union strength has declined dramatically since the early1980s in many OECD countries, which has affected wage determination.

The next section presents a simple model for the relationship between aggre-gate productivity growth and changes in the employment structure and derivesconditions for wage differentials across sectors to link up this relationship. Thesection after describes the applied data set and presents the empirical results.Furthermore, the endogeneity issue for the measure of changing employmentstructure is explored. The fourth section concludes.

A Model of Relative Wages and Growth

In order to study inter-industry wage differentials, a sectoral model is required.Moreover, imperfections in labor and product markets are called for to be able tostudy the importance of wage differentials for the relationship between aggregate

2Slaughter (2001) finds that the own-price elasticity of demand for US labor has increased in manu-facturing and five out of eight industries within manufacturing between 1961 and 1991. Internationaltrade, however, cannot be linked to the increase.

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4 A. Sørensen

productivity growth and changes in the employment structure. Such a model isdeveloped in this section.

There are two main sources for inter-industry wage differentials. One is varia-tion in the marginal value product of labor across sectors; another is variationin rents on top of marginal value products. It is established that observed rela-tive wages link up the relationship between aggregate productivity growth andchanges in the employment structure when they equal relative marginal valueproducts. Under such circumstances economic efficiency is improved when laboris reallocated from low- to high-wage sectors. The strategy in this section isto analyze how allocative efficiency depends on observable variables, implyingthat closed form solutions for wage rates, employment, value-added, and othervariables are not derived.

Wage and Price Determination

At the sectoral level, value-added is assumed to be produced according to theproduction function

Vj = Vj(Aj, Lj, Kj) (1)

where Vj is sectoral value-added, Aj is the productivity level, Lj is labor input,and Kj is capital input. The value-added function is assumed to exhibit constantreturns to scale in factor inputs and to be unit elastic with respect to productivity.One way of justifying the real value-added function is to assume that the produc-tion function of gross output is separable in real value-added and intermediateinputs, see for example Arrow (1974)3.

To determine sector wages and prices, I assume that firms bargain with sector-specific unions over wages and employment. Workers possess bargaining power inthe sense that they are able to collect a share of sector profit. Following Abowd &Lemieux (1991) and Borjas & Ramey (1995), workers receive constant fractions,γj, of profits. Consequently, firms and the union jointly maximize rents in theNash bargaining framework, where rents of sector j are given by:

πj = PjVj − ωjLj − ρjKj

πj is sector profit, Pj is the sector output price, ωj is the part of labor remunerationthat is not affected by profit sharing, and ρj is user costs of physical capital. Thesector price is determined by the inverse demand function, i.e. Pj(Vj), whichis assumed to depend negatively on own-sector price only, i.e. P′

j(Vj) < 0.4 ωj

may not equal the observed wage rate of a sector that will be denoted by ωjbecause part of labor remuneration potentially consists of labor rents. Following

3Another approach is to assume that the Hick’s aggregation theorem applies, see Diewert (1978).In this application the theorem states that the price of gross output and the prices of intermediateinputs vary in strict proportions.4ln the empirical section, I use an industry structure with broadly defined sectors, such as mining,manufacturing, construction, whole and retail trade, transportation, and finance. This implies thatthe degree of substitutability or complementarity among products across sectors is relatively low.

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Inter-industry Wage Differentials and Allocative Inefficiency 5

Borjas & Ramey (1995), ωj is assumed to equal the wage rate determined on acompetitive labor market.

Cost minimization implies that profit equals πj = (Pj(Vj) − ucj)Vj, where ucjdenotes unit costs that depend on ωj and ρj. Consequently, the price in sector j isdetermined as a mark-up over unit costs:

Pj = θ−1j ucj (2)

where the mark-up, θ−1j , equals (1 + 1/((∂Vj/∂Pj)(Pj/Vj)))

−1 and is a naturalindicator of market power.

From the cost minimization problem, labor demand is derived as:

ωj = ucjV′jL (3)

where V′jL is the marginal product of labor. Equation (3) represents the sectoral

labor demand function where the part of labor remuneration that is not affectedby profit sharing equals unit costs multiplied by the marginal product of labor,i.e. the marginal value product.

Observable sector wages, i.e. wj, are determined by the condition that the partof profits that workers receive has to be equal to the part of wages that is paid ontop of marginal value products, i.e. (wj − wj)Lj = γjπj. This implies that

wj = ϕj + γjπj

Lj= φjϕj (4)

where

ϕj = 1 + γj(θ−1j − 1)

εVj,Lj

(5)

where εVjLj is the output elasticity with respect to labor. As a consequence, sectorwages are determined as mark-ups over marginal value products with mark-upsequal to φj. Therefore, the wage curve represented by equation (4) is a negativelysloping schedule that equals or is located above the labor demand curve. Themark-up for sector j increases in bargaining power (γj), market power (θ−1

j ), anddecreases in the output elasticity with respect to labor (εVjLj).

From equations (3) and (4), relative marginal value products of labor can beexpressed as a function of relative observable wages and relative mark-ups

ucjV′jL

uckV′kL

= ωj

ωk= wj

wk/

φj

φk

It is clear that relative wages equal relative marginal value products if and only ifφj/φk = 1. This is the case when firms have no market power, i.e. θ−1

j → 1, seeequation (5), implying that product markets are perfectly competitive and firmsearn no profits. This is also the case when workers have no bargaining power,i.e. γj = 0, and get no share of profits. φj = 1 in these two cases, implying that

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6 A. Sørensen

workers are paid their marginal value product and that the sectors operate on thelabor demand curve. Finally, relative wages equal relative marginal value productswhen φj = φk > 1 for all j and k. This implies that the wage curve is above thelabor demand curve and that relative wages equal the relative marginal valueproducts. Hence, the economy operates on the relative labor demand curve. Thislatter case is a knife-edge result for the values of θj, θk, γj, γk, εVj,Lj , and εVk,Lk .

Productivity Measurement at the Aggregate Level

By maximizing aggregate value-added (∑

PjVj/P) subject to an aggregate value-added function that exhibits constant returns to scale in sector value-added,i.e. V = V(V1, V2, . . . , Vj, . . . , VJ), and (inverse) sector demand functions, theexpression for aggregate value-added growth is derived as:

V =∑

j

Pj(Vj)(1 + P′j(Vj)Vj/Pj(Vj))Vj∑

j Pj(Vj)(1 + P′j(Vj)Vj/Pj(Vj))Vj

Vj =∑

j

ucjVj

ucVVj (6)

where P and uc denote the aggregate price level of the economy and the economywide unit costs, respectively, and hatted variables denote growth rates. It is seen,that aggregate value-added growth, is a weighted average of sector value-addedgrowth rates.

Without further assumptions, growth in sectoral value-added is derived as:

Vj = Aj + V′jLLj

VjLj + V′

jKKj

VjKj (7)

using equation (1), which is substituted into equation (6). V′jK is the marginal

product of capital. As a consequence, aggregate value-added growth is expressedas:

V =∑

j

ucjVj

ucVAj +

∑j

ucjV′jL

ucVdLj +

∑j

ucjV′jK

ucVdKj (8)

Aggregate value-added growth is decomposed into three terms. The first term isaggregate productivity growth that equals a weighted average of sector produc-tivity growth rates. The second and third terms express the contributions fromgrowth in sectoral labor and capital inputs, respectively. The terms are calcu-lated by weighting sectoral inputs by marginal value products. For example, thechange in labor input of sector j, dLj, is weighted by marginal value product oflabor in sector j, ucjV′

jL. Thus, changes in inputs in sectors with high marginalvalue products have higher weights than inputs in sectors with low marginal valueproducts.

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Inter-industry Wage Differentials and Allocative Inefficiency 7

In order to focus on allocative effects of labor, I decompose the termrepresenting growth in labor input into two terms using equation (3):

∑j

ucjV′jL

ucVdLj =

∑j

ωj

ucVdLj

=∑

j

(ω

ucVdLj + (ωj − ω)

ucVdLj

)

= ωLucV

L + ωLucV

H (9)

with

H =∑

j

(ωj − ω)Lj

ωLLj

where ω denotes the aggregate marginal value product of labor. The first term onthe right-hand side is the effect on value-added growth from changing aggregatelabor quantity and the second term measures the effect from reallocation of laborinput across sectors. It is seen that reallocation of labor from sectors with lowmarginal value products to sectors with high marginal value products increaseslabor input and thereby leads to higher aggregate value-added growth:

A corresponding decomposition of capital input is performed, leading to:

∑j

ucjV′jK

ucVdKj = ρK

ucVK + ρK

ucVD

with

D =∑

j

(ρj − ρ)Kj

ρLKj

where ρ is the aggregate user costs of physical capital. Again, the first term onthe right-hand side is the effect on value added from quantity changes, whereasthe second term is the effect from quality changes.

By substitution, equation (8) is rewritten as:

V =∑

j

ucjVj

ucVAj + ωL

ucVL + ωL

ucVH + ρK

ucVK + ρK

ucVD (10)

which is the equation that is used for estimation purposes below.

Wages, Employment Structure and Growth

The purpose of this section is to investigate whether observable wage differ-entials reflect allocative inefficiency of labor input. When φj = φk, observable

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8 A. Sørensen

relative wages equal relative marginal value products, i.e. wj/wk = ϕj/ϕk, andreallocation of labor from low- to high-wage sectors will increase efficiency. Underthese circumstances, H can be expressed as:

H =∑

j

(wj − w)Lj

wLLj

that depends on inter-industry wage differentials and changes in the employmentstructure, i.e. H is based on observable variables only. I refer to this formulationof H as the reallocation index. In the following, I will include this index in growthregressions and study whether the variable contributes to explaining economicgrowth. In other words, I investigate the hypothesis that the reallocation indexbased on observable wages contributes positively and significantly to aggregateproductivity growth. If this hypothesis is not rejected, the result is consistent withobserved sector wage differentials reflecting variation in marginal value products.

The equation used for estimation purposes is a modified version of equation(10) above. The following adjustments are made. First, I exclude the qua-lity term for capital input, i.e., D, because usable sector compensation datado not exist for physical capital. Second, productivity growth is expressed asA = ∑

j ucjVjAj/ucV since Ajs are unobservable. Third, the expressions β1 =ρK/ucV and β2 = ωL/ucV are used, and an error term is added5. Finally, the con-dition that the parameters to H and L are equal is loosened such that the parameterto H is labeled β3. In the growth regressions estimated below, the restriction thatβ2 = β3 is tested.

In total, the model presented above can be expressed as:

Vct = β1Kct + β2Lct + β3Hct + Ac + εct (11)

where c is a country index, t denotes time, V is aggregate output, K is the aggregatephysical capital stock, H is the reallocation index, A is the deterministic part oftotal factor productivity, and ε is a productivity shock. Total factor productivityis defined as aggregate value-added in relation to a composite of total employ-ment and physical capital. Consequently, aggregate productivity growth equalsV − β1K − β2L, implying that it consists of the country-specific deterministicgrowth rate, Ac, the effect of a changing employment structure, β3H, and theproductivity shock, ε.

Data

The aplied data set is the OECD International Sectoral Database (ISDB), OECD(1999)6. Data are applied for 12 OECD countries: Australia, Canada, Denmark,

5ρK/ucV and ωL/ucV are estimated because the prices that enter in the ratios, i.e. ρ, ω, and uc,are unobservable.6The OECD STAN database uses a more comprehensive industrial classification, covers a longertime period (approximately 1970–99), and includes a larger group of countries than the OECD

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Inter-industry Wage Differentials and Allocative Inefficiency 9

Finland, France, (Western) Germany, Italy, Japan, Norway, Sweden, Great Britain,and the United States7. One-and four-year growth rates are determined forvalue-added, total employment, the reallocation index, and physical capital. Theapplied wage rates are average sector wages. This result in a panel data set ofgrowth rates for 12 countries over the period 1971–93. The measures of laborinput are based on hours worked, which secures that a part-time worker doesnot count as much as a full-time worker8. The OECD Input–output database,OECD (1995), is applied to construct an instrument variable used for two-stageleast square estimation.

The employment structure is organized into ten broad sectors: agriculture,mining, manufacturing, electricity, gas and water, construction, wholesale andretail trade, transportation, finance (F.I.R.E), community, social and personalservices, and government services. However, equation (11) is only estimated forthe private sector excluding agriculture because a broader measure of changingemployment structure could express the structural shift caused by growing gov-ernment sectors in OECD countries over the two decades under analysis. In thiscase, wage differentials can be present because it is difficult to evaluate the valueof labor services for government officials. Moreover, it is difficult to measurelabor compensation in agriculture due to a high share of self-employed amongthe employed persons9.

It is informative to decompose the measure of changing employment structure.The weights used in H are presented in Table 1. These weights take inter-industrywage differentials and the employment structure into account. Hence, weightsare negative for low-wage sectors and positive for high-wage sectors. The higherthe numerical value of a weight, the larger is the effect on labor allocation ofgrowing sector employment.

The main impression of Table 1 is that inter-industry wage differentials generaterelatively large variations in weights over sectors. Furthermore, the weights arerelatively persistent over time. On average, they are negative for wholesale andretail trade, and community, social and personal services. Contrarily they arepositive for mining, manufacturing, and transportation.

Table 2 presents the change in employment structure by growth differentialsbetween sector employment and total employment, i.e. Lj − L. When the growth

ISDB. However, I do not use this database because it is based on OECD ISDB for the 1970s for themajority of countries, implying that the number of industries is not increased by using this datasource. Moreover, data for the 1970s do not exist for the extra group of countries. For these reasonsand because the 1970s are of great importance to the hypothesis of the paper, I have not developednew measures based on the OECD STAN database. Another reason for not using OECD STAN isthat it is based on a different industrial classification than OECD ISDB. The latter is consistent withthe OECD Input–Output database that is used to construct an instrument variable. Input–outputtables for the countries and years included in the analysis based on industrial classification used inOECD STAN do not exist.7Belgium and the Netherlands are excluded from the analysis due to incomplete data.8The empirical results presented in this section are also established when measures of labor inputare based on persons engaged. In order to improve the clarity of the analysis, these results are notreported.9The empirical results presented in this section are also established for the total economy and privatesector. I do not present these results in the paper.

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10A

.Sørensen

Table 1. Weights based on inter-industry wage differentials, presented in percent

AUS CAN DNK FIN FRA WGR ITA JPN NOR SWE GBR USA AVG(%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)

AGR 1971 −3.1 −2.8 −4.9 −4.4 −7.1 −3.2 −10.4 −11.7 −7.9 −2.2 −1.3 −1.9 −5.11981 −2.2 −1.7 −2.0 −1.7 −2.9 −2.2 −5.2 −8.6 −5.1 −1.5 −1.0 −1.7 −3.01991 −2.0 −1.7 −1.8 −2.6 −1.4 −1.7 −4.4 −5.6 −4.0 −1.1 −0.6 −1.1 −2.3

MID 1971 0.6 0.1 0.0 0.0 0.0 0.3 N.A 0.2 0.1 0.0 0.0 0.2 0.11981 0.9 0.4 0.0 0.1 0.2 0.3 N.A 0.0 0.7 0.0 0.3 0.6 0.31991 0.9 0.3 0.0 0.0 0.0 0.2 N.A 0.0 1.5 0.0 0.3 0.3 0.3

MAN 1971 1.2 0.8 −2.3 0.2 3.4 1.2 2.2 5.1 1.7 −0.5 0.1 3.0 1.41981 1.2 0.7 −0.3 0.4 2.3 2.3 1.8 2.9 1.9 −0.5 2.1 3.9 1.61991 0.6 0.5 −1.1 0.1 2.3 4.1 2.1 3.1 2.4 0.5 3.1 2.9 1.7

EGW 1971 0.4 0.0 0.1 0.2 0.4 0.3 1.0 0.6 0.3 −0.1 0.0 0.3 0.31981 0.2 0.2 0.1 0.2 0.4 0.5 0.7 0.6 0.2 −0.2 0.6 0.4 0.41991 0.4 0.3 0.1 0.2 0.5 0.5 0.7 0.6 0.3 0.1 0.4 0.4 0.4

CST 1971 2.2 3.1 1.7 2.7 0.1 −0.2 −1.2 0.7 −0.2 1.1 −0.3 1.4 0.91981 2.6 4.2 0.3 1.0 −0.2 −0.7 −0.8 0.5 −1.2 1.4 −0.2 0.9 0.71991 2.8 2.9 0.4 1.9 −0.2 −0.6 −0.9 1.2 −1.4 2.4 0.3 0.4 0.8

RET 1971 −4.0 −5.0 0.8 −2.6 −0.3 −2.4 −1.3 −2.3 −0.9 −0.3 −2.5 −2.9 −2.01981 −5.9 −5.9 0.9 −0.8 −1.6 −2.4 −2.7 −3.9 −0.7 −0.1 −4.1 −4.3 −2.61991 −6.2 −7.5 1.2 −1.8 −1.3 −2.5 −3.3 −6.2 −0.3 0.1 −6.2 −5.9 −3.3D

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2014

Inter-industryW

ageD

ifferentialsand

Allocative

Inefficiency11

TRS 1971 0.9 −0.2 0.2 0.7 1.0 1.0 2.7 2.9 4.1 0.7 1.1 1.3 1.41981 0.3 0.7 −0.2 0.0 0.7 0.3 2.1 2.1 3.2 0.1 1.1 1.8 1.01991 −0.1 −0.1 −0.2 −0.2 0.3 0.0 1.1 1.9 1.1 −0.2 2.2 1.0 0.6

FNI 1971 0.8 −0.7 1.0 1.0 2.3 0.7 2.7 1.6 1.2 1.1 3.0 0.4 1.31981 −0.3 0.7 0.4 1.0 2.4 0.9 2.6 2.0 1.1 1.4 2.8 0.1 1.31991 1.9 1.1 1.1 1.0 3.3 1.2 2.4 2.4 1.8 1.5 5.3 2.2 2.1

SOC 1971 −1.8 10.8 −0.2 −1.8 −0.7 −1.2 0.4 −2.7 −1.7 −2.1 −0.9 −3.0 −0.41981 1.0 6.7 −0.4 −1.6 −1.5 −1.7 −0.6 −1.9 −1.9 −1.7 −2.6 −3.1 −0.81991 0.6 11.0 −0.3 −0.6 −1.7 −2.6 −1.5 −3.7 −2.2 −1.8 −7.0 −2.5 −1.0

PGS 1971 2.8 −6.7 4.6 4.4 0.9 3.6 4.2 5.3 3.3 2.4 −1.2 1.2 2.11981 2.2 −6.2 1.3 1.6 0.2 2.9 3.1 5.8 1.8 0.7 −0.8 1.3 1.21991 1.1 −7.3 0.6 2.3 1.8 1.8 5.0 5.8 0.7 −2.2 −0.8 2.4 0.6

Notes: Australia (AUS), Canada (CAN), Denmark (DNK), Finland (FIN), France (FRA), West Germany (WGR), Italy (ITA), Japan (JPN), Norway (NOR), Sweden (SWE),Great Britain (GBR), and the United States (USA). Agriculture, hunting, forestry & fishing (AGR), mining and quarrying (MID), manufacturing (MAN), electricity, gas andwater (EGW), construction (CST), wholesale & retail trade, restaurants & hotels (RET), transport, storage & communication (TRS), F.I.R.E (FNI), community, social &personal services (SOC), and producers of government services (PGS). Other producers (OPR) is excluded from the table.Sources: ISDB, OECD (1999).

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Table 2. Growth rates of sector employment, deviation from growth in total employment (percentage)

AUS CAN DNK FIN FRA WGR ITA JPN NOR SWE GBR USA AVG(%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%)

AGR 1971−80 −2.0 −0.9 −0.2 −2.3 −1.0 −2.8 1.3 −0.5 −0.9 0.6 −0.5 0.4 −0.91981−90 −1.5 −6.2 −1.3 −2.5 −1.9 −2.6 −0.4 −1.7 −1.5 −1.4 −2.2 −2.3 −4.21991−93 −2.0 −7.0 −2.1 −3.5 −2.7 −2.7 −1.3 −2.2 −2.6 −3.1 −3.3 −3.6 3.1

MID 1971−80 −0.7 1.4 5.7 −0.5 3.0 −3.0 N.A. −6.7 20.2 −1.3 4.6 −0.4 2.11981−90 −1.1 −0.2 10.6 −2.1 2.3 −1.8 N.A. −3.9 8.3 −4.4 0.4 −1.0 0.71991−93 −2.0 −3.5 3.5 −4.6 −6.1 −6.2 N.A. −3.3 4.7 −1.8 1.6 −6.1 −2.2

MAN 1971−80 −2.0 −0.9 0.2 −0.2 −0.6 −0.9 0.0 −2.3 −1.3 −0.2 −0.2 0.6 −0.71981−90 −2.7 −0.5 0.4 −0.4 −0.3 −1.2 −0.3 0.2 −1.0 −0.7 −1.2 −0.2 −0.61991−93 −1.5 −1.8 −0.1 −1.3 −0.7 −0.8 −1.0 0.5 −0.9 −2.0 −2.1 0.1 −0.7

EGW 1971−80 1.0 1.4 0.2 0.8 1.5 1.5 0.5 −0.7 −1.6 0.1 −0.6 0.3 0.41981−90 −4.1 0.7 2.1 −0.9 1.0 0.5 0.6 −0.1 −0.8 0.1 −1.2 0.2 −1.21991−93 −3.9 1.6 0.4 −0.4 −1.2 −0.6 1.3 −0.2 −1.6 −1.1 −0.4 −0.1 −0.5

CST 1971−80 −0.8 1.0 0.2 −1.7 0.4 −2.1 0.4 2.1 14.1 −0.1 −0.4 −0.2 0.91981−90 −0.6 0.3 0.3 −0.1 −1.7 −3.8 −0.1 0.5 −0.2 0.2 −2.1 −4.4 −1.01991−93 −0.9 0.4 −2.6 −4.5 −2.2 0.9 −1.4 2.0 −2.7 −1.1 −2.4 −2.4 −1.3

RET 1971−80 −0.1 −0.8 0.2 −1.3 0.1 −0.2 0.4 0.9 0.3 0.5 0.6 0.7 0.21981−90 0.6 0.0 1.0 0.2 1.0 −0.2 0.7 0.3 0.6 2.3 1.9 1.4 0.91991−93 0.8 1.5 −0.1 0.1 1.0 1.7 0.6 −0.1 0.1 0.5 1.3 1.5 0.9D

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TRS 1971−80 −0.3 −1.9 −0.6 0.3 1.1 0.4 0.8 −2.8 −3.0 0.1 −0.3 −0.9 −0.51981−90 −0.6 −1.3 0.4 −3.1 −0.2 0.0 1.8 −2.0 −4.4 0.1 −1.7 −1.8 −1.01991−93 −2.6 −0.1 1.7 −1.5 0.1 −0.6 2.2 −2.3 −3.7 −0.2 −0.5 −2.2 −0.8

FNI 1971−80 1.8 0.8 −0.1 0.7 −0.1 −0.1 −0.6 0.8 0.2 −0.1 0.5 0.2 0.31981−90 2.9 1.0 −0.1 0.8 −0.4 0.0 −1.1 −0.5 0.3 0.2 0.6 0.5 0.31991−93 0.1 0.9 −0.3 0.6 −0.3 −0.1 −0.8 −0.7 −1.4 1.1 −0.1 0.2 −0.1

SOC 1971−80 3.1 −0.8 −0.4 1.1 1.7 5.0 0.9 2.9 2.7 0.3 −0.5 1.5 1.41981−90 1.4 0.2 2.1 0.5 4.1 4.0 1.8 7.2 2.4 2.7 −0.6 1.4 2.11991−93 1.9 0.3 2.5 1.8 4.3 2.9 2.0 4.7 3.9 3.6 0.7 0.9 2.3

PGS 1971−80 1.8 −0.9 0.5 −0.1 −0.2 0.3 −0.3 1.7 0.2 −0.3 −1.0 −1.2 0.01981−90 0.3 −1.2 −0.7 0.7 0.9 −0.2 −0.5 0.2 0.2 −0.7 −0.6 −1.0 −0.31991−93 0.8 −0.5 −0.9 1.2 1.6 −0.6 −0.4 0.4 2.0 −1.9 2.8 0.2 0.3

Notes: Australia (AUS), Canada (CAN), Denmark (DNK), Finland (FIN), France (FRA), West Germany (WGR), Italy (ITA), Japan (JPN), Norway (NOR), Sweden (SWE),Great Britain (GBR), and the United States (USA). Agriculture, hunting, forestry & fishing (AGR), mining and quarrying (MID), manufacturing (MAN), electricity, gas andwater (EGW), construction (CST), wholesale & retail trade, restaurants & hotels (RET), transport, storage & communication (TRS), F.I.R.E (FNI), community, social &personal services (SOC), and producers of government services (PGS). Other producers (OPR) is excluded from the table.Sources: ISDB, OECD (1999).

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Figure 1. Growth in GDP versus growth in employment, physical capital, and the reallocation index.Note: ρ presents the pairwise correlation coefficients between value-added growth and growth inthe relevant input. p-values testing the null of independence are in parentheses (an asterisk denotessignificance at 0.01 level or better). Source : OECD (1999).

differential is positive for a sector, sector employment increases as a share of totalemployment.

The data show that the employment structure changes over time. For example,employment in agriculture, manufacturing, and transportation fall on average asa share of total employment, whereas increases are observed for sectors such asmining, wholesale and retail trade, and F.I.R.E.

The overall impression of Tables 1 and 2 is that the employment structureis changing and that inter-industry wage differentials contribute to importantdifferences in sector weights used to construct Hct. Before performing the formalgrowth regressions, I assess the potential for the reallocation index to yield resultsthat attribute a significant role for output growth.

In Figure 1, one-year growth rates of aggregate value-added are plotted againstgrowth rates of total employment, reallocation of labor, and physical capitalAt first sight, it seems that both employment and reallocation of labor haveimportant roles to play. The simple (pooled) correlation coefficients equal 0.67and 0.21 between aggregate value-added growth and employment growth, andbetween GDP growth and the reallocation index, respectively.

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Inter-industry Wage Differentials and Allocative Inefficiency 15

Both coefficients are significantly different from zero at the 1% level. Themeasure of changing employment structure thus seems to be important for outputgrowth. Furthermore, the accumulation of physical capital may be important,which is indicated by a (pooled) correlation coefficient of 0.37, which is alsosignificantly different from zero.

Growth Regressions

The relationship between value-added growth and growth in production fac-tors presented in the panel equation, i.e. equation (11), is estimated using OLSwith fixed country effects. Several empirical findings for inter-industry wagedifferentials are important for the chosen estimation method. These are thatinter-industry wage differentials are quite stable across space, that industry wagepatterns are remarkably similar among countries with diverse labor market insti-tutions, and that inter-industry wage differentials exist to about the same extent inunion and non-union environments (see Krueger & Summers, 1988, and Katz &Summers, 1989).

The estimated panel equations include a dummy variable for each year tocontrol for economy-wide movements. The models are estimated for one–andfour-year growth rates, where the latter cover five time periods (1971–1974,1975–1978, 1979–1982, 1983–1986, and 1987–1990). The advantage of the fixed-effect model is that the deterministic part of aggregate productivity growth iscountry-specific, which is less restrictive than under cross-country growth regres-sions where the deterministic part is identical across countries (see Islam, l995).Equation (11) is estimated with and without the logarithm to lagged labor produc-tivity, i.e. log (Vct−τ /Lct−τ ). The variable is included to control for productivityconvergence among the countries. The inclusion of this lagged variable may beproblematic because it is difficult to find suitable conversion factors for measuringrelative value-added for narrow definitions of the economy (see Sørensen, 2001).In the analysis, expenditure purchasing-power parities for total GDP are used.

Table 3 presents the results for the growth regressions for the full period1971–1993. The equations are estimated with and without fixed country effectsfor the productivity parameter A. Regression 1 includes a deterministic part ofproductivity that is invariant over countries, whereas Regression 2 is estimatedusing fixed country effects. The same is the case for Regressions 3 and 4, Regres-sions 5 and 6, Regressions 7 and 8. Moreover, Regressions 3, 4, 7, and 8 includelagged labor productivity, whereas the remaining regressions do not. Regressions1, 2, 3, and 4 are based on one year growth rates, whereas the remaining are basedon 4 year growth rates. It is seen that the estimated coefficients to the realloca-tion index are positive for all regressions. However, the coefficients are mainlysignificant for models with invariant country effects.

Two additional results from Table 3 should be mentioned. First, the parametervalues to lagged labor productivity are negatively and significantly different fromzero at the 10% level. Hence, countries with relatively low labor productivitygrow faster than countries at a higher stage of development and thereby catch-upon the leader country. This is a standard result in the empirical growth literature

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Table 3. Regressions of economic growth on production factors, 1971–93. (Dependent variable: value-added growth.)

One-year Four-year

Without log (V−τ /L−τ ) With log (V−τ /L−τ ) Without log (V−τ /L−τ ) With log (V−τ /L−τ )

(1) (2) (3) (4) (5) (6) (7) (8)Constant A Fixed effects, Ai Constant A Fixed effects, Ai Constant A Fixed effects, Ai Constant A Fixed effects, Ai

dlogH 1.33∗∗ (0.53) 1.03∗ (0.61) 1.34∗∗ (0.54) 0.94 (0.62) 1.53 (0.94) 0.78 (1.43) 1.67∗∗ (0.81) 0.79 (1.41)dlogL 0.51∗∗∗(0.05) 0.61∗∗∗(0.06) 0.55∗∗∗(0.06) 0.63∗∗∗(0.06) 0.42∗∗∗(0.07) 0.71∗∗∗(0.09) 0.52∗∗∗(0.08) 0.74∗∗∗(0.08)dlogK 0.26∗∗∗(0.08) 0.06 (0.12) 0.17∗∗ (0.09) −0.02 (0.13) 0.34∗∗∗(0.10) 0.06 (0.16) 0.22∗ (0.12) −0.06 (0.16)log(V−τ /L−τ ) −0.02∗∗∗(0.01) −0.03∗ (0.01) −0.06∗∗ (0.03) −0.13∗ (0.06)R2 adjusted 0.66 0.68 0.67 0.69 0.63 0.71 0.66 0.72Sample size 276 276 276 276 60 60 60 60

Notes: Dependent variable: dlogV refers to the growth rate of real value added. dlog X refers to the log difference in variable X. Explanatory variables: dlogH is the reallocationindex, dlogL is the growth rate of hours worked, and dlogK is the growth rate of aggregate physical capital. log(V−τ ) is lagged labor productivity. Four-year changes arebased five time periods (1971–1974, 1975–1978, 1979–1982, 1983–1986, and 1987–1990). One-year and four-year models are estimated, using OLS/fixed effects. All regressionsinclude a full set time dummies. White Heteroscedasticity consistent standard errors are in parentheses. ∗∗∗1% confidence level, ∗∗5% confidence level, and ∗10% confidencelevel.Sources: OECD (1997a, 1997b, 1999), and Statistics Denmark (1999).

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see for example Barro & Sala-i-Martin (1992) and Dowrick & Nguyen (1989)10.The deterministic part of productivity growth, Ac, is not shown in the table.The estimated results show that the variation in Ac, is relatively high, and thehypothesis of identical country effects, i.e Ac = A, is rejected at the 5% level forall models. Consequently, the fixed effects formulation of equation (11) is usedin the following. The fixed country effect is relatively low for the United States,which is also in line with results in the convergence literature where the UnitedStates is found to be the leader country, see for example Bernard & Jones (1996).Hence, the fixed country effects contain additional information on convergenceamong OECD countries that is left unexplained by lagged labor productivity.

Second, physical capital growth enters insignificantly in regressions with fixedeffects. When equation (11) is estimated with the restriction that Ac is invari-ant across countries, physical capital growth enters positively and significantlyin explaining output growth11. The explanation is that time series for physicalcapital are smooth and therefore it is difficult statistically to distinguish betweena time trend and the time series. Since the hypothesis that Ac = A for all c isrejected, I use fixed country effects and exclude physical capital growth ratesfrom the regressions when they enter insignificantly.

In the following, the full period 1970–1993 is split into the sub-periods 1970sand 1980s because the estimated parameter for H, i.e. β3, is expected to enterpositively and significantly for the 1980s, whereas this may not be the case for the1970s. This expectation is motivated by the idea that bargaining power has erodedfor unskilled labor from 1970s to 1980s. This may have happened as an indirecteffect of globalization that has increased the effective elasticity of labor demand.Moreover, globalization and other effects may directly have increased competi-tion pressures in product markets. See for example Bertrand (2004), Borjas &Ramey (1995), Rodrik (1997), and Wallerstein & Western (2000). An alternativeexplanation is that skill-biased technological changes reduce bargaining powerbecause such changes increase the competitive wage rate of skilled workers andthereby undermine the coalition between skilled and unskilled workers in the sup-port of unions, see Acernogiu et al. (2001). Both explanations lead to a decreasingrelative wage of unskilled labor due to falling labor rents.

The suggestion that bargaining power has eroded and market power hasdecreased from the 1970s to the 1980s, implies that the economy has moved

10The driving mechanisms behind convergence are of course important. Two potential candidatesare decreasing returns to the set of reproducible factors of production, which implies high relativereturns to investments for countries on low stages of development, and technological spillovers fromleader countries. Mankiw et al. (1992) find support for the former explanation such that the accu-mulation of human and physical capital is important for (conditional) convergence. Benhabib &Spiegel (1994) on the other hand investigate diffusion of technology between countries and find thatthe stock of human capital of a country affects the speed of adoption of technology from abroad.Based on the empirical analysis of the present paper, however, it is not possible to distinguish theimpact of the different mechanisms.11Islam (1995) also finds that the elasticity of output with respect to capital is much lower when fixedcountry effects are applied. However, the estimates are still significant for the group of countries inhis study.

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closer to the case with γj = γK = 0 and θj = θk = 1. This suggests that the sectorshave moved towards being located on the labor demand curve during the 1980s,whereas the scenario that applies for the 1970s is less clear. As a consequence theregression analysis should be carried out separately for the two decades.

The results for sub-periods are presented in Table 4. Only one-year modelsare included due to the low number of observations for four-year models12. Thecoefficients to the reallocation index are positively and significantly different fromzero at the l% level for the two models in the 1980s, see Regressions 3 and 4. Onthe other hand, the hypothesis that the coefficient equals zero cannot be rejectedfor the 1970s.

Table 4, and Regressions 1–4 paint a clear picture for the relationship betweenaggregate productivity growth and reallocation of labor. For the 1970s, the real-location index for labor does not contribute to explaining aggregate productivitygrowth. The opposite result is established for the 1980s, where the realloca-tion index enters positively and significantly in explaining aggregate productivitygrowth13.

A dummy variable is introduced for countries with high union density, a largeshare of workers covered by a collective bargaining agreement in 1990, andhigh degree of centralized wage-setting. This country group includes Denmark,Finland, Sweden, and Norway. The data on union density and workers covered bya bargaining agreement come from Wallerstein & Western (2000), whereas dataon degree of centralized wage-setting come from Calmfors & Driffill (1988).

Regressions 5–8 include the dummy for countries with strong union environ-ments. It is evident that the point estimates for the reallocation index are fairlysimilar for the two country groups. For the 1970s, the reallocation index entersinsignificantly for both country groups, see Regressions 5 and 6. The coefficientsto the reallocation index are positive but insignificant for countries with strongunion environment. For the 1980s, the point estimates are of similar magnitudefor the two country groups, whereas the significance is higher for the countrieswith weak union environment (significant at the 1% level for countries with weakunion environment and 10% level for countries with strong union environment).The main impression is that there is no difference in results for the two countrygroups14.

12In Table 4, the later sub-period is 1981–90. Extending this period to 1981–93 does not change theresults.13One concern related to the results presented in Table 4 is that the level of aggregation of sectorsis too crude and should be based on a higher number of industries. To deal with this concern,I have constructed an alternative measure of H including manufacturing industries; not just themanufacturing sector. Instead of using 10 broadly defined sectors with manufacturing being oneaggregate sector, the alternative measure uses between 9 and 13 manufacturing industries for eachcountry, implying a total number of industries between 19 and 23. It is possible to construct themeasure with 19 industries for 6 countries and 23 industries for 5 countries. Australia is excludedfrom the analysis owing to incomplete data. The main result presented in this paper is also validusing this alternative measure. In order to keep the exposition as clearly as possible, these resultsare not presented.14An alternative group of countries with strong union environment contains Denmark, Finland,Germany, Italy, Norway, and Sweden. The presented results in Table 4, Regressions 5–8 are insensitiveto changing country groups.

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Table 4. Regressions of economic growth on the reallocation index and growth in hours worked. (Dependent variable: value-added growth)

1971–80 1981–90 1971–80 1981–90

(1) (2) (3) (4) (5) (6) (7) (8)

dlogH 0.25 (1.14) 0.16 (1.14) 3.72∗∗∗(1.04) 3.76∗∗∗(1.02)D∗dlogH 4.33 (2.85) 4.29 (2.81) 3.64∗ (2.06) 3.63∗ (2.05)(1 − D)∗ dlogH −0.68 (1.10) −0.80 (1.11) 3.75∗∗∗(1.17) 3.79∗∗∗(1.13)dlogL 0.62∗∗∗(0.10) 0.64∗∗∗(0.10) 0.55∗∗∗(0.06) 0.53∗∗∗(0.06) 0.61∗∗∗(0.10) 0.63∗∗∗(0.10) 0.55∗∗∗(0.06) 0.053∗∗∗(0.06)log(V−τ /L−τ ) −0.04 (0.04) 0.05 (0.05) −0.04 (0.04) 0.05 (0.05)

R2 adjusted 0.69 0.69 0.66 0.66 0.70 0.70 0.65 0.65Sample size 120 120 120 120 120 120 120 120

Notes: Dependent variable: dlog V refers to the growth rate of real value added. dlog X refers to the log difference in variable X. Explanatory variables: dlogH is thereallocation index, and dlogL is the growth rate of hours worked. logV−τ /L−τ is lagged labor productivity. D denotes a country dummy equal to one for Denmark,Finland, Norway, and Sweden. The models are estimated using OLS/fixed effects. All regressions include a full set of time dummies. White Heteroscedasticity consistentstandard errors are in parentheses. ∗∗∗1% confidence level, ∗∗5% confidence level, and ∗10% confidence level.Sources: OECD (1997a, 1997b, 1999), and Statistics Denmark (1999).

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Table 5. Regressions of economic growth on the reallocationindex and growth in hours worked. Estimated parameterto the reallocation index, dlogH. (Dependent variable:value-added growth)

Break year T 1971-T (T + 1)-1990

1977 0.17 2.27∗∗1978 −0.21 2.57∗∗1979 −0.86 3.94∗∗∗1981 0.34 3.99∗∗∗1982 0.15 4.15∗∗∗1983 0.24 3.67∗∗∗

Notes: Dependent variable: dlogV refers to the growth rate ofreal value added. dlogX refers to the log difference in variable X.Explanatory variables: dlogH the reallocation index and dlogL isthe growth rate of hours worked. The estimated equation includesfixed effects and a fill set of time dummies. White heteroscedastic-ity consistent standard errors are in parentheses. ∗∗∗1% confidencelevel, ∗∗5% confidence level, and ∗10% confidence level.Sources: OECD (1997a, 1997b, 1999), and Statistics Denmark (1999)

A Wald test for the restriction that β2 = β3 is rejected at the 5% level for allmodels. The possible explanation for this result is that the theoretical model onlydistinguishes labor by sectoral affiliation. In reality, labor input is much more het-erogeneous and employment should by divided into groups with characteristicssuch as sex, age, employment class, education etc, besides sectoral affiliation. Thisis the method applied in modern growth accounting, see for example Jorgensonet al. (1987) and Ho & Jorgenson (2000). In the present analysis, however, the focalpoint is the wage structure of average workers across sectors and the expectedconsequence is that the variation in H is lower than for a corresponding mea-sure constructed on a sequence of background variables because much of theheterogeneity vanishes. As a consequence, β3 is expected to exceed β2.

To investigate whether the results presented in Table 4 are robust to changesin the break point year, I have estimated the regressions using all years between1977 and 1983 as break point years. As is evident from Table 5, the qualitativeconclusions presented in Table 4 hold for all break years at the 5% level. Thisresult leads me to conclude that the main result presented in the paper is robustto the break point choice.

Endogeneity

An important objection to the results presented above is that labor allocation maybe influenced by aggregate productivity growth itself. The association betweenH and aggregate productivity growth may not represent a causal relationshipwhere reallocation of labor between sectors with different marginal value prod-ucts of labor changes productivity. This causality is a requirement for the aboveinterpretation to be valid. Changes in productivity could potentially affect the

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inter-industry wage structure. It is possible, for example, that productivitychanges in the 1980s are biased towards high-wage sectors for exogenous rea-sons, and it is those sectors that expand and draw labor. In this case, a positiveand significant coefficient on H can arise even if inter-industry wage differentialsdo not reflect reallocative inefficiencies.

An often used method to analyze the question of endogeneity is instrumen-tal variables using two-stage least square estimation (TSLS). A good instrumentshould be highly correlated with the reallocation index and uncorrelated withthe disturbance term. I introduce an instrument that is based on the assumptionthat the production function of sectoral gross output is separable in intermedi-ate inputs and real value-added. This is one of two approaches of justifying areal value-added function as discussed above. When gross output is separablein intermediate inputs and real value-added, an increase in intermediate inputshas a direct positive effect on gross output but no direct effect on value-added.However, it seems likely that higher intermediate inputs are positively correlatedwith primary-factor inputs and especially labor input, e.g. intermediate input insector j is positively correlated with labor input of sector j.

Following these lines, the variable Mct is defined according to

Mct =∑J

j=1(wjct − wct)Ljct

wctLctXjct (12)

which is expected to be highly correlated with the reallocation index. Xj denotesthe growth rate of intermediate input in sector j. Furthermore, the instrument vari-able Mct is expected to be uncorrelated with the unexplained part of productivitygrowth; that is the error term of equation (11).

Table 6, Regression 2, is based on two-stage least square estimation. The samplesize is reduced to six countries; Canada, Denmark, France, Japan, Great Britain,and the United States. It is evident from stage one of the TSLS estimation that Hand M are positively and significantly correlated at the 5% level. Furthermore,the part of H that is explained by M (and the exogenous explanatory variables)enters positively and significantly in stage two of the TSLS regression. This sug-gests that reallocation of labor to high-wage sectors leads to higher productivitygrowth. The OLS regression for the same sample as used in the TSLS regressionis presented in Regression 1. It is seen that the point estimate for H is determinedwith lower precision under the TSLS estimation. This is a well-known character-istic of TSLS. It is, however, evident that 95%-confidence intervals for the pointestimate for H under the two estimation methods overlap.

An alternative method to address the question of endogeneity of H is basedon the logic that sector wages and sector productivity growth rates are positivelyand significantly correlated if productivity changes are biased towards high-wageindustries. Therefore, sector productivity growth is regressed on relative sectorwages separately for each country using OLS with sector-specific intercepts. Eachequation incorporates a full set of time dummies to control for common timeeffects. I use several alternative measures of sector productivity growth. These are

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22 A. Sørensen

Table 6. Regressions of economic growth on the reallocation index andgrowth in hours worked, OLS and two-stage least square. (Dependentvariable: value-added growth), 1981–90

(2) TSLS

(1) OLS Stage 1 Stage 2

dlogH 4.87∗∗∗(1.48) 7.94∗∗ (3.62)dlogL 0.58∗∗∗(0.08) −0.02 (0.01) 0.63∗∗∗(0.09)dlogK 0.11∗ (0.06)dlogM 0.28∗∗(0.13)R2 adjusted 0.65 0.57 0.62Sample size 57 57 57

Notes: Dependent variable: dlogV refers to the growth rate of real value-added.dlogX refers to the log difference in variable X. Explanatory variables: dlogHis reallocation index, dlogL is the growth rate of hours worked, dlogK is thegrowth rate of aggregate physical capital, and dlogM is the instrument variable.The models are estimated using OLS/fixed effects. All regressions include fixedeffects and a full set of time dummies. White heteroscedasticity consistent standarderrors are in parentheses. ∗∗∗1% confidence level, ∗∗5% confidence level, and ∗10%confidence level. Countries included are Canada, Denmark, France Japan, UnitedKingdom, United States.Sources: OECD (1995, 1997a, 1997b, 1999), and Statistics Denmark (1999).

measures of total factor productivity growth and growth of labor productivity,capital productivity, and value-added. The measure of total factor productivitygrowth is based on total labor compensation as a share of aggregate value-added.

The results of these regressions are presented in Table 7 for the period 1981–90.The table presents the sign of the coefficient to sector wages where – (+) indicatesthat this coefficient is negative (positive). Moreover, the table specifies if the coef-ficients are significantly different from zero or not. For example, the results showthat the correlation between sector labor productivity growth (V/L) and sectorwages in France (FRA) is negative and that this coefficient is insignificant.

Table 7. Regressions of sector productivity growth rates on sector wages- one year averages, 1981–90.(Dependent variable: sector productivity growth)

AUS CAN DNK FIN FRA WGR ITA JPN NOR SWE GBR USA

TFP + + − −∗ − −∗∗ − − +∗∗ + − +V/L + + − −∗ − −∗∗ − − +∗ + − +∗∗V/K + + − − − − + − +∗∗ + −∗ −V − +∗ − + + − + − + + −∗∗ +Notes: Dependent variable: sector productivity growth rates. TFP: total factor productivity growth based onlabor costs as a share of aggregate value added, V/L: labor productivity growth, V/K: capital productivitygrowth, and V: value added growth. Explanatory variables: :Wic refers to the wage rate of sector i in relationto the average wage in country c. The models are estimated using OLS/fixed effects. All regressions includea full set of time dummies. + indicates a positive parameter value, − indicates a negative parameter value.∗∗∗1% confidence level, ∗∗5% confidence level, and ∗10% confidence level.Sources: OECD (1997a, 1997b), ISDB OECD (1999), and Statistics Denmark (1999).

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Inter-industry Wage Differentials and Allocative Inefficiency 23

The main impression of Table 7 is that sector productivity growth and sectorwages are not clearly related, suggesting that endogeneity of H is not a problem15.

Conclusion

The purpose of this paper is to investigate the hypothesis that a reallocation indexof labor enters positively and significantly in explaining aggregate productivitygrowth. The reallocation index is defined as a weighted average of the changein sectoral employment using inter-industry wage differentials as weights. If thehypothesis cannot be rejected, this implies that economic efficiency is improvedwhen labor is reallocated from low- to high-wage sectors.

Using a panel data set for 12 OECD countries over the period 1971–93, laborallocation is found to contribute to aggregate productivity growth. This resultis especially strong for the 1980s. Contrarily, it did not contribute significantlyto productivity growth during the 1970s. This result is consistent with wage dif-ferentials reflecting variation in marginal value products of labor across sectorsin the 1980s but not in the 1970s. Moreover, it is consistent with the view that aregime shift took place in the wage-setting behavior for developed countries fromthe 1970s to the 1980s.

One important objection to the above interpretation is that the causality couldbe the other way around; that is, aggregate productivity changes could potentiallyaffect the inter-industry wage structure. To study the importance of this potentialendogeneity problem, I introduce an instrument variable based on the that sectoralintermediate input and labor input is highly correlated; in expanding sectors bothintermediate and labor inputs increase and vice versa. On the other hand, value-added is not directly affected by changing use of intermediate input because ofseparability of sectoral gross output into intermediate input and sectoral value-added. I find that productivity growth is positively related to the reallocationindex when using two stage least square estimation. Moreover, sector productivitygrowth rates are not highly positively correlated with sector wages. This suggeststhat the endogeneity problem is modest.

There are two broader implications of the results presented in this paper. First,the method for analyzing sector wage differentials has the advantage that it enablesus to learn about allocative inefficiency of labor. Data with a relatively longtime span can be applied, which can make estimation for sub-periods possible.If the results for the reallocation index change over time, it is consistent withchanging wage-setting behavior. Of course, this latter result is only suggestive butcomplements more traditional research on inter-industry wages.

Second, the practice of measuring elasticities of labor types by value shares isput into question. This method builds on the assumption that wages are equal tomarginal value products of labor. This practice is often used in modern growthaccounting, see Jorgenson et al. (1987), Ho & Jorgenson (2000), and OECD(2001). The present study suggests that the practice seems reasonable for lateryears; however, such measures should not be used for early years.

15The only country that has strong positive correlation between sector productivity growth andsector wages is Norway. This correlation is driven by the mining sector.

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24 A. Sørensen

Acknowledgements

The author wishes to thank George J. Borjas, Svend E. Hougaard Jensen,Tryggvi Thor Herbertsson, Sunwoong Kim, Hans Christian Kongsted, Morten I.Lau, Dani Rodrik, Jonathan Skinner, Torsten Sløk, Jan Rose Skaksen, PeterBirch Sørensen, two anonymous referees, and seminar participants at the JohnsHopkins University, University of Copenhagen, Copenhagen Business School, andCEBR for helpful discussions. The usual disclaimer applies

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Appendix

Compensation of Total Employment

Compensation of employees comes from OECD (1999), Compensation of sectoremployment is determined by assuming that self-employed workers receive thesame compensation as sector employees on average. That is,

Comp. of sector employment = LEmployees

Comp. of employees in sector

I depart from this assumption in some industries and countries because the com-pensation of total employment exceeds value-added on average for the period1970–93. In such cases, I follow OECD (1999)16 and set the share of compen-sation of sector employment out of value-added equal to the sample mean forthe remaining countries. Such adjustments are performed for wholesale and retailtrade in Japan, construction in Norway, and community, social and personalservices in Finland.

Total Hours Worked

Hours worked at the sector level are calculated in two steps. In the first step,sector employment is converted to full-time equivalent persons. In the secondstep, sector hours worked are determined using sector employment measured infull-time equivalent persons and average hours worked per full-time equivalentpersons for the total economy.

16p. 31 footnote 8.

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26 A. Sørensen

Employment in full-time equivalent persons are calculated according to

LFTj =

(em

j (1 − 0.5pm) + efj (1 − 0.5pf )

)Lj

where LFT denotes full-time equivalent persons, em and ef denote the male andfemale shares out of total employment, and pm and pf are male and female part-time frequencies17. It is assumed that a part-time worker works half the time ofa full-time worker.

Total hours worked for the total economy is given by

HW = Lhw

where HW is the aggregate hours worked for the total economy and hw is the aver-age hours worked per person in employment for the total economy. Accordingly,the average hours worked per full-time equivalent person for the total economy,hwFT, is

hwFT = HW/LFT

Finally, hours worked at the sector level are determined according to

HWj = LFTj hwFT

The construction of hours worked requires additional statistical sources. Theseare: OECD (1997a, b) (male and female employment in full-time equivalent per-sons), and Statistics Denmark (1999) (hours worked for Denmark). It has notbeen possible to obtain data for Belgium on hours worked.

Instrument Variable

Data for the instrument variable stem from the input–output database, (OECD,1995). This database provides input–output tables for selected years over theperiod 1968–90. Since I address endogeneity for the period 1981–1990, I includecountries from the database that have at least three input-output tables for1980, mid-1980, and 1990. Countries that qualify for this requirement are:Canada (1981, 1986 and 1990), Denmark (1980, 1985, 1990), France (1980, 1985,1990), Japan (1980, 1985, 1990), Great Britain (1979, 1984 and 1990) and theUnited States (1982, 1985 and 1990).

The input–output tables are used to calculate Mjct for the years mentionedabove. For the years in between, I determine Mjct by

Mcalcjct =

(Mjct

Mct

)calc (Mct

VAct

)calc

VAct

where calc indicates a calculated variable. Calculated variables are determined bylog-linear interpolation between years for which input–output tables exist. Theinstrument variable is then constructed according to equation (12).

17Part-time frequencies for women and men are observed for 1973, 1979, 1983, 1990, 1991, 1992,and 1993. For other years, part-time frequencies are determined by linear interpolation.

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